Next, we explain the inductive idea used by Wilf [1]}.
Let \(x\)  be a leaf of \(T\)  and \(y\)  its neighbour.
Let \(u_1, u_2, \ldots , u_r\)  be the neighbours of \(y\)  different from \(x\) .
Let \(U_i\)  be the component (subtree) of \(T \setminus \lbrace x,y\rbrace \)  that contains \(u_i\) , and let \(W_{i,j}\) , \(1 \le j \le s_i\) , be the components of \(U_i \setminus u_i\) .
Finally, let \(w_{i,j}\)  be the neighbour of \(u_i\)  belonging to \(W_{i,j}.\) 
This is illustrated in Figure REF .
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